Question

The difference between the wave number of $1^{st}$ line of Balmer series of paschen series for ${Li}^{2+}ion$ is:

• A. $\frac{R}{36}$
• B. $\frac{5R}{36}$
• C. $4R$
• D. $\frac{R}{4}$

Answer 1

Answer: (D)

$\frac{R}{4}$

$\begin{array}{c}\frac{1}{\lambda }=R{t}^2\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]\\ 1stlineofpolymerseries=\alpha \to 3\\ Lastnofpolymerseries=3\to \infty \\ L_1^{st}=t=3\\ {\overline{V}}_B-{\overline{V}}_L=R{\left(3\right)}^2\left[\frac{1}{{\alpha }^2}-\frac{1}{3^2}\right]-R{\left(3\right)}^2\left[\frac{1}{3^2}-\frac{1}{\infty }\right]\\ =R{\left(3\right)}^2\left[\frac{1}{4}-\frac{1}{9}-\frac{1}{9}\right]\\ =R\times 9\left[\frac{1}{4}-\frac{2}{9}\right]\\ =R\times 9\times \frac{9-8}{36}\\ {\overline{V}}_B-{\overline{V}}_L=R\times 9\times \frac{1}{26}\\ Thedifference=\frac{R}{4}\end{array}$

Hence, Option $D$ is correct.